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Hat Matrix

A matrix, H, arising in multiple regression, which is used to obtain the predicted values of the response variable corresponding to each observed value via the equation

                                                                                  ŷ = Hy

The matrix H puts the ‘hats’ on the elements of y; it is a symmetric matrix and is also idempotent.

Given explicitly in terms of design matrix, X as

                                                                                 𝐻 = 𝑋(𝑋’𝑋)−1𝑋

The diagonal elements of H are often useful diagnostically in assessing the results from the analysis. 

Hat Matrix

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